Deciphering oxygen distribution and hypoxia profiles in the tumor microenvironment: a data-driven mechanistic modeling approach.

Objective. The distribution of hypoxia within tissues plays a critical role in tumor diagnosis and prognosis. Recognizing the significance of tumor oxygenation and hypoxia gradients, we introduce mathematical frameworks grounded in mechanistic modeling approaches for their quantitative assessment within a tumor microenvironment. By utilizing known blood vasculature, we aim to predict hypoxia levels across different tumor types.Approach. Our approach offers a computational method to measure and predict hypoxia using known blood vasculature. By formulating a reaction-diffusion model for oxygen distribution, we derive the corresponding hypoxia profile.Main results. The framework successfully replicates observed inter- and intra-tumor heterogeneity in experimentally obtained hypoxia profiles across various tumor types (breast, ovarian, pancreatic). Additionally, we propose a data-driven method to deduce partial differential equation models with spatially dependent parameters, which allows us to comprehend the variability of hypoxia profiles within tissues. The versatility of our framework lies in capturing diverse and dynamic behaviors of tumor oxygenation, as well as categorizing states of vascularization based on the dynamics of oxygen molecules, as identified by the model parameters.Significance. The proposed data-informed mechanistic method quantitatively assesses hypoxia in the tumor microenvironment by integrating diverse histopathological data and making predictions across different types of data. The framework provides valuable insights from both modeling and biological perspectives, advancing our comprehension of spatio-temporal dynamics of tumor oxygenation.

A minimal model for hepatic fatty acid balance during fasting: application to PPAR alpha-deficient mice.

The purpose of this study is to identify the hierarchy of importance amongst pathways involved in fatty acid (FA) metabolism and their regulators in the control of hepatic FA composition. A modeling approach was applied to experimental data obtained during fasting in PPARalpha knockout (KO) mice and wild-type mice. A step-by-step procedure was used in which a very simple model was completed by additional pathways until the model fitted correctly the measured quantities of FA in the liver. The resulting model included FA uptake by the liver, FA oxidation, elongation and desaturation of FA, which were found active in both genotypes during fasting. From the model analysis we concluded that PPARalpha had a strong effect on FA oxidation. There were no indications that this effect changes during the fasting period, and it was thus considered to be constant. In PPARalpha KO mice, FA uptake was identified as the main pathway responsible for FA variation in the liver. The models showed that FA were oxidized at a constant and small rate, whereas desaturation of FA also occurred during fasting. The latter observation was rather unexpected, but was confirmed experimentally by the measurement of delta-6-desaturase mRNA using real-time quantitative PCR (QPCR). These results confirm that mathematical models can be a useful tool in identifying new biological hypotheses and nutritional routes in metabolism.

Qualitative analysis of the relation between DNA microarray data and behavioral models of regulation networks.

We introduce a mathematical framework that allows to test the compatibility between differential data and knowledge on genetic and metabolic interactions. Within this framework, a behavioral model is represented by a labeled oriented interaction graph; its predictions can be compared to experimental data. The comparison is qualitative and relies on a system of linear qualitative equations derived from the interaction graph. We show how to partially solve the qualitative system, how to identify incompatibilities between the model and the data, and how to detect competitions in the biological processes that are modeled. This approach can be used for the analysis of transcriptomic, metabolic or proteomic data.

Carcinoid tumor of the ileum with perforation and infiltration of the abdominal wall.

The carcinoid tumor presented was noteworthy in several respects. It attained a large size within the space of only two months and was so extensive that it penetrated the abdominal wall. Despite its great size there were no liver metastases, and at no time did the patient exhibit any of the signs or symptoms of the carcinoid syndrome.

The surgical treatment of the Zollinger-Ellison syndrome: an update.

Forty-six professors of surgery in answers to a questionnaire reported that 143 patients with Zollinger-Ellison syndrome had been admitted to their hospitals within the last 2 years. The bed capacity of these hospitals totaled 27,019. In extrapolating these figures, it is seen that the capacity of the 46 institutions averaged 587 beds per hospital, and that an average 71.5 patients with Zollinger-Ellison syndrome were admitted each year. In other words, a hospital with 587 beds might expect 1.55 yearly admissions of patients suffering from this disease. Two surgical methods have emerged as today's main treatment choices for Zollinger-Ellison syndrome that is unaccompanied by isolated gastrinoma. These are 1) preoperatively administered H2 blockers followed by less-than-total gastrectomy, truncal vagotomy, and postoperative H2-blocker therapy; and 2) preoperatively administered H2 blockers followed by highly selective vagotomy plus postoperative H2-blocker therapy. Only seven of 46 respondents still maintain that total gastrectomy should be carried out to cure the disease. All respondents advocate excision of an isolated gastrinoma as the treatment of choice if one is found at surgery.

Reduction of dynamical biochemical reactions networks in computational biology.

Biochemical networks are used in computational biology, to model mechanistic details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as combinatorial explosion are strong obstacles against analyzing the dynamics of large models of this type. Multiscaleness, an important property of these networks, can be used to get past some of these obstacles. Networks with many well separated time scales, can be reduced to simpler models, in a way that depends only on the orders of magnitude and not on the exact values of the kinetic parameters. The main idea used for such robust simplifications of networks is the concept of dominance among model elements, allowing hierarchical organization of these elements according to their effects on the network dynamics. This concept finds a natural formulation in tropical geometry. We revisit, in the light of these new ideas, the main approaches to model reduction of reaction networks, such as quasi-steady state (QSS) and quasi-equilibrium approximations (QE), and provide practical recipes for model reduction of linear and non-linear networks. We also discuss the application of model reduction to the problem of parameter identification, via backward pruning machine learning techniques.

Dynamical robustness of biological networks with hierarchical distribution of time scales.

Concepts of distributed robustness and r-robustness proposed by biologists to explain a variety of stability phenomena in molecular biology are analysed. Then, the robustness of the relaxation time using a chemical reaction description of genetic and signalling networks is discussed. First, the following result for linear networks is obtained: for large multiscale systems with hierarchical distribution of time scales, the variance of the inverse relaxation time (as well as the variance of the stationary rate) is much lower than the variance of the separate constants. Moreover, it can tend to 0 faster than 1/n, where n is the number of reactions. Similar phenomena are valid in the nonlinear case as well. As a numerical illustration, a model of signalling network is used for the important transcription factor NFkappaB.